Surfaces of constant curvature in with isolated singularities

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• 作者：José ; A. Gá ; lvez^a ; ^{jagalvez@ugr.es} ; Laurent Hauswirth^b ; ^{laurent.hauswirth@univ-mlv.fr} ; Pablo Mira^c ; ^{pablo.mira@upct.es} ; ^{laflipo@gmail.com}
• 关键词：Surfaces of constant curvature ; Isolated singularities ; Conical singularities ; Monge&ndash ; Ampè ; re equation ; Harmonic maps ; Geometric Cauchy problem ; Peaked sphere
• 刊名：Advances in Mathematics
• 出版年：2013
• 出版时间：10 July, 2013
• 年：2013
• 卷：241
• 期：Complete
• 页码：103-126
• 全文大小：334 K

文摘

We prove that finite area isolated singularities of surfaces with constant positive curvature in are removable singularities, branch points or immersed conical singularities. We describe the space of immersed conical singularities of such surfaces in terms of the class of real analytic closed locally strictly convex curves in with admissible cusp singularities, characterizing when the singularity is actually embedded. In the global setting, we describe the space of peaked spheres in , i.e. compact convex surfaces of constant curvature with a finite number of singularities, and give applications to harmonic maps and constant mean curvature surfaces.